Damped sine wave

A damped sine wave is a sinusoidal function whose amplitude approaches zero as time increases.

Damped sine waves are commonly seen in science and engineering, wherever a harmonic oscillator is losing energy faster than it is being supplied.

Sine waves describe many oscillating phenomena. When the wave is damped, each successive peak decreases as time goes on.

A true sine wave starting at time = 0 begins at the origin (amplitude = 0). A cosine wave begins at its maximum value due to its phase difference from the sinewave. In practice a given waveform may be of intermediate phase, having both sine and cosine components. The term "damped sine wave" describes all such damped waveforms, whatever their initial phase value.

The most common form of damping, and that usually assumed, is exponential damping, in which the outer envelope of the successive peaks is an exponential decay curve.

The general equation for an exponentially damped sinusoid may be represented as:

where:

which can be simplified to

Where:

Other important parameters include:

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